Cold water in winter will make the hose on your hose reel less flexible so will effect the flow of water through it.
Daqua once posted that reducing hose size from minibore to microbore will reduce flow by 30%. Microbore is half the size of minibore.
Your battery won't be performing as well as it does when the weather is warmer which will also add to the pump's lethargy.
You don't mention what pump you have, but we have got Shurflos on my van one of which is 11 years old and the other 12 years old and still working well.
If you have let a pump's internals freeze up then the diaphragm could be damaged or displaced.
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